Field of the Invention (Technical Field):
The attitude dynamics of a spacecraft with an actuated variable speed control moment gyroscope (VSCMG), is derived using the principles of variational mechanics. The model of the VSCMG preferably comprises an offset between the gimbal frame's center of mass and the flywheel or rotor's center of mass. The dynamics equations show the complex nonlinear coupling between the internal degrees of freedom associated with the VSCMG and the spacecraft base body's attitude degrees of freedom. This dynamics model is then further generalized to include the effects of multiple VSCMGs placed in the spacecraft base body, and sufficient conditions for non- singular VSCMG configurations are obtained. A control scheme using a finite number of VSCMGs for attitude stabilization maneuvers in the absence of external torques and when the total angular momentum of the spacecraft is zero is presented. Embodiments of the present VSCMGs optionally utilize inertia variations of the gimbal on which the flywheel is mounted. These gyroscopes can be used for attitude actuation in space vehicles, including small spacecraft, for precise pointing control, re-orientation, and detumbling maneuvers. It can be used in both government agency-sponsored missions (for example for NASA, ESA, JAXA, ISRO, etc.) and the commercial space industry. Because of the optimization of control authority with respect to the same control inputs, embodiments of the present invention can be used for automobiles, robotics, health care (balance assistance), in addition to attitude control for spacecraft, astronauts (such as those on a spacewalk), and maritime vehicles.
Background Art:
Note that the following discussion may refer to a number of publications and references. Discussion of such publications herein is given for more complete background of the scientific principles and is not to be construed as an admission that such publications are prior art for patentability determination purposes.
Internal momentum exchange devices can be used as spacecraft attitude actuators to stabilize a desired attitude or track a desired attitude profile. A Control Moment Gyroscope (CMG) is a momentum exchange device consisting of a rotor running at a constant angular speed, mounted on a gimbal frame structure that can be rotated at a controlled rate. CMGs are used to generate the required momentum for attitude (orientation) control of spacecraft, including attitude stabilization of agile spacecraft. They can be categorized as Single Gimbal Control Moment Gyroscopes (SGCMGs) or Double Gimbal Control Moment
Gyroscopes (DGCMGs). A Variable Speed Control Moment Gyroscope (VSCMG) combines the features of a constant speed SGCMG with a rotor whose angular speed can be varied. Defining features and comparisons between SGCMGs and DGCMGs are given in Wie, B., 2008, Space Vehicle Dynamics and Control, 2nd ed. American Institute of Aeronautics and Astronautics, Reston, Va. VSCMGs are described in Schaub, H., and Junkins, J. L., 2009. Analytical Mechanics of Space Systems, 2nd ed. AIAA Education Series, Reston, Va., October; McMahon, J., and Schaub, H., 2009. “Simplified singularity avoidance using variable speed control moment gyroscope nullmotion”. AIAA Journal of Guidance, Control, and Dynamics, 32(6), Nov.-Dec., pp. 1938-1943; and Yoon, H., and Tsiotras, P., 2002. “Spacecraft adaptive attitude and power tracking with variable speed control moment gyroscopes”. AIAA Journal of Guidance, Control and Dynamics, 25, pp. 1081-1090.
Single Gimbal CMGs typically produce larger torques for the same actuator mass compared to reaction wheels. However, the dynamics of CMGs is more complex than that of reaction wheels, with inherent singularities in the map between the inputs (gimbal rates) and outputs (angular momentum or torque acting on spacecraft bus) (i.e. the CMG cannot produce a desired control torque vector). Most of the available steering laws that locally produce instantaneous control torques, have difficulties avoiding singularities in minimally redundant SGCMG systems. Most of the existing (VS)CMG dynamics models use some simplifying assumptions in their formulation. These assumptions are: (1) the offset between the rotor center of mass (CoM) and the gimbal axis (or CoM) in the direction of the rotor's rotation axis is zero i.e., σ=0; (2) both the gimbal and the rotor-fixed coordinate frames are their corresponding principal axes frames, the rotor is axisymmetric, and both rotor and gimbal inertias are about their respective center of masses (i.e., Jr=JrCoM and Jg=JgCoM); (3) the gimbal frame structure has “negligible” inertia (i.e., Jg≃0); (4) the angular rate of the gimbal frame is much smaller (“negligible”) compared to the rotor angular rate about its symmetry axis (i.e., {dot over (α)}(t)<<{dot over (θ)}(t)); and (5) for a CMG, the speed of the rotor {dot over (θ)} is constant (i.e., the VSCMG is operated as a standard SGCMG).
In the present invention, a more general dynamics model of a spacecraft with VSCMG is obtained without using most or any of these assumptions. Since the configuration space of attitude motion of a spacecraft with internal actuators is a nonlinear manifold, the global dynamics of this system is preferably treated using the formulation of geometric mechanics. This model is obtained using variational mechanics, and in the framework of geometric mechanics on the nonlinear state space of this system. The dynamics model is thereafter generalized to a spacecraft with a finite number of VSCMGs. The dynamics model obtained here is applicable to VSCMGs with non-axisymmetric rotors and gimbals, where the rotation axis of the rotor may be offset from the center of mass of the gimbal structure. While it is true that existing VSCMG designs may not require these properties when manufactured, it is possible that during installation within a spacecraft bus or during the course of operations they become misaligned, in which case this generalized model and the control schemes based on it would still apply.